Certification Assistance for Marine Engineers

Canadian
First Class ME Applied Mechanics

In Canada, Transport Canada administers the Marine Engineering
examination process; visit the
Training Page for details on the process. The actual exam consist of nine
(9) questions randomly drawn from a question bank of the various subject. Six
(only) must be answered in a 3.5hrs time frame. The exam questions are similar
to these, presented below, and are drawn heavily from similar question in the
Reed's Marine Engineering series of books.

Disclaimer

Transport Canada has ask us to advise users of this webpage to keep in
mind that these questions are not the exact questions found in their
exams. Martin's Marine Engineering Page -
www.dieselduck.net is not affiliated with
Transport Canada and these questions have been gathered from various
sources.

1. A conical pendulum has a bob of 2 kg mass attached to the
end
of a piano wire 1.5 m long. It
is set in notion with a horizontal circular radius of 500 mm.

1) find the
angular velocity

2) the time
to make one complete revolution of the bob

3) the
tension in the wire

Ans: 2.6338 rad/s
Ref Reeds p118

Ans: 2.3856
seconds Ref
JUN89

Ans: 20.8 N
Ref MAR92

2. The stabilizing gyroscope of a ship has a mass of 50
tonnes,
a radius of gyration of 1.525 m, and rotates about a vertical
axis at 900 rev/min. Calculate:

1) the time
required to attain full speed after starting from rest, if the gyro is
supplied with a constant power input
of 75 kW

2) the
torque required to cause precession about the axis in a vertical fore and
aft plane at the rate of 1o/s note:

power = Iw(alpha)

torque = Iw(omega) where

I = moment
of inertia (kg m2)

w =
velocity of spin (rad/sec)

(alpha) =
angular acceleration (rad/s2)

(omega) =
velocity of precession

Ans: 3.825
hours Ref DEC87

Ans: 191.27
Ref JUL89

3. Using
strain energy methods, find the mass of a spring required
to stop a truck of mass 10 tonnes, travelling at 0.91 m/s. Assume that there is no compression on the spring before
contact with the truck.

note: C(steel) = 7380 kg/m3

G(steel) = 85 GPa

T(steel) = 280 MPa

Ans: 132.4
kg

Ref MAY89
Ref FEB91

4. An axial thrust of 50 kN is carried by a plain collar
type
thrust bearing having inner and outer diameters of 250
mm and 400 mm respectively. Assuming
that the coefficient of friction between the thrust surfaces is 0.02, and
that the local wear rate of these surfaces is proportional to the pressure
and to the rubbing speed, determine the power
absorbed in friction of 120 rev/min.

Ans: 2.04
kW

Ref Hannah
p209
Ref specimen

5. During a test on a car, the following information was obtained.

Velocity
(m/s) 0 1.2 3.25 6.4 10.2 13.6 15.2
16.0

Time
(seconds) 0 2.0 4.0 6.0 8.0
10.0 12.0 14.0

1) Sketch
the velocity/time graph

2) find the
velocity at 3.5 seconds

3)
calculate the distance travelled after 14 seconds

note: graph
paper is required for this question

Ans: 4 m/s
Ref MAY89

Ans: 112 m
Ref JUL89

Ref FEB91

6. A small air compressor is belt driven from a lay shaft in a
workshop. The pulley on the compressor being 300 mm in diameter, and
the angle of lap of the belt is 165o. When the belt is moved from the loose to the fast pulley, it slips
for 8 seconds until the compressor attains its constant speed of 300
rev/min. The flywheel of the compressor has a moment of inertia
of 4 km m2 and the friction requires a constant torque
of 4 Nm. If the coefficient
of friction is 0.28 during the acceleration period,

1) find the
tensions in both reaches of the belt, and also

2) the
distance that the belt slips and the energy lost in that time due to the
belt slip.

note T1 =
euo T2

Ans: 237.4
N Ref
Hannah p220

Ans: 106 N
Ref specimen

Ans: 18.84
m

Ans:
2475.58 J

7. A belt drive consists of two v-belts in parallel, on grooved
pulleys of the same size. The
angle of the groove is 30 degrees. The cross sectional area of each belt is 750 mm2 and u =
0.12. The density of the belt material is 1.2 Mg/m3 and the maximum
safe stress in the material is 7 MN/m3.

Calculate;

1) the
power that can be transmitted between pulleys of 300 mm diameter rotating at 1500 rev/min.

2) the
shaft speed in rev/min at which the power transmitted would be at maximum

Ans: 171.66
kW Ref
Hannah p217

Ans: 2807.7
rev/min Ref
JAN88

Ref MAR91

8. A beam of uniform cross section has a uniformly distributed load of
200 N/m length, it also carries loads as shown. Draw the shearing force and bending moment diagrams.

PUT
DIAGRAM HERE !

Ref FEB84
Ref JUN87

9. A sluice gate of mass 6 tonnes, is subjected to a normal pressure
of 2.5 MN. It is raised by
means of a vertical screw which engages with a screwed bush fixed to the
top of the gate. The screw is rotated by a 37 kW motor running at a maximum
speed of 600 rev/min, a bevel pinion on the motor shaft gearing with a
bevel wheel of 80 teeth keyed to the vertical screw. The screw is 125 mm mean diameter and 25 mm
pitch. The u for the screw in the nut is 0.08 and between the gate and its
guides is 0.10. If friction
losses, additional to those mentioned above amount to 15% of the total
power available, determine the maximum number of teeth for the bevel
pinion.

Ans: 14
teeth Ref
Hannah p195

Ref
specimen

10. A gear box is to be arranged for four speeds in approximate
geometrical progression, one of which is to be a direct drive. The driving shaft transmits 30 kW at 2400 rev/min, and the
speed of the driven shaft in lowest gear is to
be approximately 400 and the layshaft is 180 mm and all teeth
are 6 module. Find:

1) the
necessary number of teeth in each pair of gears

2) the
torque on the driven shaft

3) the
torque on the gear-box frame in lowers gear neglecting friction

12. The pressure on the piston of an engine is 1800 kPa when the crank
has turned through an angle of 30 degrees past top dead centre.
The piston diameter is 220 mm and the ratio of connecting rod
length to crank is 4.5. Determine
either graphically or by calculation:

1) the
thrust in the connecting rod

2) the
force required to overcome the friction of the guide

Ans: 68.883
kN Ref
specimen

Ans: 188.86
N

13. A curved stationary vane has an inlet angle of 30 degrees and an
outlet angle of 20 degrees, both angles being measured
from the normal to the vane. If
the vane can withstand a force of 2 kN, determine the maximum diameter of
a water jet allowed tangentially on to the inlet of the vane when the
supply of water is from a reservoir 20 meters above the vane. Neglect friction and other losses in the pipe joining the
nozzle to the reservoir and at the nozzle. Take density of water as 1000 kg/m3

Ans: 60 mm
Ref specimen

14. The distance between the axles of a tanker milk truck is 2.56 m and
its center of gravity is 2.45 m above the ground under fully loaded
conditions. Calculate the
speed at which the tanker will overturn when traveling around a bend of 50
m radius. Assume that the road is smooth and flat.

Ans: 57.63
km/hr Ref Reeds p111

Ref MAY89
Ref FEB91

15. Three masses A, B, and C of 1.5 kg, 2.0 kg, and 2.5 kg are arranged
as illustrated. The
coefficient of friction between B and the table surface is 0.2 and there
is negligible friction in the pulleys. Starting from rest, find the velocity of B after it has traveled 1
meter.

PUT DIAGRAM
HERE !

Ans 1.4 m/s
Ref JAN88

Ref JUN89
Ref JUL89

16. A ship is pitching 10 degrees above and 10 degrees below the
horizontal. Assuming the
motion to be simple harmonic, having a period of 12 seconds, find the maximum angular
velocity and
angular acceleration of the ship during pitching.

Ans: 0.0914 rad/s
Ref Hannah p79

Ans:
0.04785 rad/s2 Ref
JAN88

Ref JUN89

17. 1)
State what is meant by the parallel axis theorem.

2) The
second moment of area of a rectangle about an axis through its centroid
and parallel to the base is given by: BD3 12

Calculate
the polar second moment of a square section of
side "s"

Ans: s4

Ref: Hannah
p86
Ref DEC87

18. A ball
of 2 kg mass traveling at a velocity of 22 m/s overtakes another ball of
mass 4.0 kg traveling in the same direction as the first ball but with a
velocity of 10 m/s. In elastic conditions prevail and the coefficient of
restitution is 0.80, calculate the velocity of the two balls after
collision.

Ans:
a) 17. 2 m/s Ref: Hannah, pg 8

b) 7.6 m/s
Ref DEC87

19. A
torsional pendulum consists of a wire 0.5 m long, 10 mm diameter, find at
its upper end and attached at its lower end to a heavy disk having a
moment of inertia of 0.06 kg m2. The
modulus of rigidity of the wire is 44 GN/m2. Find the frequency of
torsional oscillation of the disk. If
the maximum displacement to one side of the rest position is 5 degrees
find the maximum angular velocity and acceleration of the
disk.

Ans:
a) 6.039 Hz

b) 3.31 rad/s

c) 125.61 rad/s2

Ref Hannah p78

20. A
venturi meter is placed in a horizontal section of a pipeline, 120 mm
diameter. The water pressure measured upstream of the meter is 700 kPa and
at the throat of the meter, 650 kPa. The throat diameter is 60 mm and the
coefficient of discharge is 0.98. Calculate the rate of the flow through
the pipe (m3/s).

Ans: 0.0286
m3/s

Ref FEB84
Ref JUN89

21. The
impeller of a centrifugal pump has an outside diameter of 1000 mm, and
inside diameter of 500 mm, and a vane entrance width of 170 mm. The radial
velocity of the water through the impeller is 2.0 m/s when the pump
rotates at 300 rev/min Calculate:

1) The
width of the impeller vane at exit.

2) The
angle of the impeller vane at entrance so that
water enters without shock.

Ans:
1) 85 mm Ref DEC83

2) 14.29o
Ref DEC85

Ref DEC87
Ref JUL89

22. A canning machine has a particular
component of mass 2.5 kg moving with SHM of amplitude 400 mm and
130 oscillations per minute. Calculate:

1) The
maximum accelerating force upon the component,

2) The
accelerating force when the component is displaced 300 mm from mid
position.

Ans:
1)185.2 N Ref
FEB84

2)138.9 N
Ref MAY89

Ref FEB91
Ref APR91

23. A tank
with sides 2 m long contains 1 m of sea water of density 1.024], with 0.6
m of oil [density 0.8] above. Calculate the force on one side of the tank
and the position of the centre of pressure.

worm square
threaded. Determine the input torque on the worm spindle and the overall
efficiency.

Ans:
a) 496.8 Nm Ref Hannah
p192

b) 36%
Ref APR85

Ref DEC86

25. A
figure skater has just gone into a pirouette on one skate with both arms
and other leg and foot extended. In this position, her angular velocity
and moment of inertia are:

[W = 2 pi rad/s] [I = 4.5 kg/m2]

Neglect
friction, calculate her angular when she pulls into the fast spin
position. The moment of inertia during fast spin is 1.2 kg m2

Ans: 23.56 rads/s
Ref DEC83

Ref MAR91

26. A
girder of uniform cross section is 8 m long and supports a informal
distributed load of 400 kN. The girder is supported by three columns at
the centre and both ends such that all support points are at the same
level.

1)
calculate the reactions in the columns

2) sketch
the bending moment diagrams.

note: the
deflections [S1] at midspan due to a uniformly distributed load W and
deflection [S2] sue to force P in outer columns are:

s1 = 5WL3
s2 = PL3
384EI
48EI

Ans:
R1 = R2 = 75 kN Ref Reeds
R3 = 250 kN
Ref DEC85

27. A steel
bar 30 mm diameter and 400 mm long is placed inside a brass tube. Outside
diameter 40 mm and inside diameter 32 mm. The tube is 0.125 mm longer than
the bar. This compound bar placed between rigid plates arranged so that
the axial compressive force of 50 kN can be applied to the assembly.
Calculate the stress set up in the tube and bar. Es = 200 GPa,
Eb
= 90 GPa

Ans: os =
40.96 MPa Ref
FEB84

ob = 46.556
MPa Ref
JAN88

28. A
machine is driven through a reduction gear of ratio 9:1 by an electric
motor. The armature, pinion and shaft which has a mass moment of inertia of 0.5 kg m2. The mass moment of
inertia of the machine components is 40 kg m2. The torque developed by the
motor when starting from rest is 30 Nm, the reduction gear efficiency is
95%. Calculate:

1) the
brake power developed by the motor to drive the machine at a constant speed of 160 rev/min.

2) the time
required for the speed of the machine to reach
60 rev/min from rest.

Ans:
a) 1.764 kW Ref Hannah p28

b) 3.15 s
Ref DEC87

Ref MAY89
Ref FEB91

29. A
venturi meter having an inlet diameter of 100 mm and a throat diameter of
30 mm is fitted to a pipe line conveying liquid of density 850 kg/m3. A
mercury "U" tube is fitted between inlet and throat, and the
surfaces of separation have a difference of
levels of 200 mm. Assuming a discharge coefficient of 0.96, calculate the
mass of flow of the liquid.

note: the
density of mercury is 13.6 x 103 kg/m3

Ans: 4.44
kg/s

30. 1)
Sketch the controlling force for a Porter type governor using centripetal
force for the ordinate and radius for the abscissa.

2) Sketch
the controlling force for a Hartwell type governor
using a similar coordinate system. a) Illustrate stable, unstable, and
isochronous conditions.

3) A Porter
type governor has 300 mm arms and the rotating balls each have a mass of
1.8 kg. At the mean speed of 120 rev/min, the arms are at a angle of 30
deg to the vertical axis. Calculate the central dead load of the governor.

Ans: 5.728
kg Ref Hanna p155

Ref DEC83

31. A joint is held together by a cotter having a taper of 1:10 equally
divided between the two edges. The cotter has a coefficient of friction,
u, of 0.18 and is driven into the joint by a force of 500 N. Calculate the
force:

1)
fastening the joint together.

2) required
to eject the cotter.

Ans:
a)1077.7 N Ref Reeds pg 159
b) 277.6 N Ref Dec87

32. 1)
Derive an expression for the maximum shear stress "T" for a
closed-coiled helical spring, where the mean diameter is "D", the wire diameter is "D" and
the axial load "W".

2) A
close-coiled helical spring has an axle load of 90 N and the mean diameter
is 8 times the diameter of the wire
Allowing a maximum shear stress of 105 MPa, find the diameter of the wire.

Ans:
1) T = 8WD Ref JUN89
pi d3
2) 4.18 mm

33. An
engine is designed to develop 10 kW of power at a mean speed of 1000
rev/min. Find the moment of inertia in kg m2, of a suitable flywheel,
assuming a speed variation of 1.5% of the mean speed and an energy
fluctuation equal to 0.9 of the work done per revolution.

Ans: 1.664
kg m2 Ref: Reeds pg 104

34. Water
is pumped from a fire engine to the nozzle of a hose being used to fight a
fire, the nozzle is 30 m above the pump outlet. The nozzle outlet diameter
is 25 mm and the velocity of the water pumped through it is 28 m/s. Determine the quantity of water flowing through the nozzle per
second and the power of the pump if losses are neglected. Take density of
water as 1000 kg/m3.

Ans:
a) 13.7445 kg/s
b) 4045 W

35. A
Reciprocating engine having a stroke of 600 mm operates at 400 rev/min.
calculate the velocity and acceleration of the piston when the crank has
turned 30 deg. past top dead center. neglect the effect of connecting rod
angularity.

Ans:
a) 6.28 m/s Ref DEC83
b) 455.86 m/s2 Ref DEC85

36. A
spring of stiffness 200 N/m and 0.75 kg mass is set in motion when a mass
of 5 kg is attached to the free end. calculate the oscillations:

1) when the
spring mass is excluded.

2) when the
spring mass is included.

note: 1/3
of spring mass has effect on the hook.

Ans:
1) 1.006 Hz. Ref Hannah p67
2) 0.982 Hz. Ref JAN88

37. A
uniform ladder rest on a rough horizontal deck leaning against a rough
vertical bulkhead. When the ladder makes an angle of 60 deg. to the deck,
it is just on the point of slipping. If the coefficient of friction
between the foot of the ladder and the deck is 0.27 calculate the
coefficient of friction between the top of the ladder and the bulkhead.

Ans: 0.24
Ref Reeds p588

38. A
turnbuckle has right hand single start square threads of 8 mm pitch, 28 mm
pitch diameter, and the coefficient of friction between screw and nut is
0.15. The device is used to tighten a steel stay having a cross sectional
area of 80 mm2, a length of 46 m and a modulus of elasticity, E=140 GPa.
If the stay is preloaded to 1.8 kN. Calculate:

2) A solid
shaft 150 mm diameter is to be replaced by a hollow shaft of similar
material of same length and have the same mass. The strain energy taken by
the hollow shaft is 20% greater
torque than can be taken by the solid shaft with the same stress. Find the
outside and the inside diameter of the hollow shaft.

Ans:

Ref Reeds
#13-13
Ref JUL89

40. A tank
10 m long, 4 m wide, and 6 m high is filled with oil (rd 0.9) and the oil
rises to a height of 5 m up a vertical pipe above the top of the tank.
Calculate the load on one end plate and on the bottom of the tank.

Ans:
a) 1695.17 kN Ref Reeds p331
b) 3884.76 kN

41. A bolt
and nut falls into a deep tank and the sound of the splash when it strikes
the liquid is heard after 2.2 seconds. Estimate the ullage of the tank if
the velocity of the sound is 335 m/s a the ambient temperature of the air.

Ans: 22.32
m Ref
specimen

42. The
blades of a three blade propeller has masses of 10.20, 10.25 and 10.20 kg
. Their centers of gravity are 300 mm, 299 mm and 301 mm respectively from
the center of rotation. the angles are all 120 degrees. Calculate the out of balance
force developed at 8000 rev/min.

Ans: 62 N
Ref FEB84

43. A
cylindrical pressure vessel as the longitudinal seam welded in the form of
a helix. The helical seam is inclined at an angle of 56 degrees to the
circumferential seam, the inside diameter of the vessel is 1.8 m, the
shell thickness 34 mm, and the working pressure is 3500 kPa. Calculate:

1) the
tensile stress normal to the circumferential seam.

2) the
tensile stress normal to the oblique seam.

Ans:
a) 52.5 MN/m2 Ref specimen
b) 8.58 MN/m2

44. A
satellite is placed in a circular orbit 650 km above the earth's surface
at a latitude of 45 degrees. At sea level, g = 9.80665 m/s2, and the
earth's mean radius is 6380 km.

1)
calculate the speed to maintain the orbit.

2) find the
period of one revolution.

Ans:
1) 27127 km/hr Ref DEC83
2) 1.628 hr Ref DEC85

Ref FEB90
Ref MAR91

45. A
container of mass 2 tonnes is being lowered by a winch at the rate of 0.6
m/s. The cable supporting the load has a cross sectional area of 1200 mm2
and a modulus of elasticity of 200 GPa. When 15 m of cable has been
unwound from the which drum, the brake is suddenly applied.

1) find the
maximum stress in the cable due to sudden braking.

2)
find the maximum extension of the cable.

Ans:
a) 89.44 MN/m2 Ref DEC83
b) 6.71 mm
Ref DEC85

Ref JUN89
Ref JUL89

46. A
flywheel has a mass of 100 kg, radius of gyration 0.8m diameter of 0.8 m.
It increases speed from 50 rev/min to 2000 rev/min in 10 seconds. Find the
accelerating torque.

Ans: 1306.9
Nm Ref
JAN88

47. A
spherical gas storage tank is 25 m diameter and constructed of 18 mm
plate, the welded seams of which may be considered as being 90% of the
plate strength. The yield strength of the material is 245 MPa and a factor
of safety of 2.5 is deemed adequate. Calculate the maximum permissible
pressure the sphere may safely withstand.

Ans: 254
kPa
Ref
DEC87

Ref MAY89
Ref FEB90
Ref FEB91

48. A
balloon is rising with a velocity of 5 m/s when a sand bag, used for
ballast, is released. At the instant when the sand bag is released, the
balloon is 420 m above the earth. Calculate the time required for the sand
bag to reach the ground.

Ans: 9.78
seconds Ref DEC87

49. A cone
clutch has a mean surface diameter of 300 mm a face width of 65 mm, and
the inclined angle between the friction faces s 30 deg. The clutch lining
as a coefficient of friction, u=0.3, and the normal pressure acting upon
the surface is 70 pa. Calculate:

1) the
maximum power that can be transmitted when rotating at 1200 rev/min.

note:
assume uniform wear theory.

Ans: 22.9
kW
Ref
Hannah p202

Ref DEC87
Ref DEC89
Ref MAR91

50. The
diagram shows a belt drive fitted with a gravity idler. The driver rotates
anti-clockwise at 360 rev/min and the coefficient of friction between the
belt and pulley is 0.3. Determine the initial belt tension and the power
transmitted. Neglect any lag in the belt.

Ans:
a) 175.7 N Ref Hannah p 222
b) 1987 W
Ref JAN88

Ref JUN89
Ref FEB90

Insert
diagram here

51. A mass
of 10 kg is laying on a smooth (frictionless) surface of a wheel inclined
at 30 degrees. It is attached
by a wire 2 m in length parallel to the plane to centre of the wheel.
The wheel revolves at 10 rev/min. Find the tension in the wire.

Ans:
Ref MAY89

Ref JUL89
Ref FEB91

52. A
police car equipped with a radar speed detecting device observes a
motorist travelling at a speed of 120 km/hr. The police car starts pursuing the motorist 30 seconds after the
initial observation and accelerates to 160 km/hr during a 20 second time
interval. Assume both
vehicles maintain their speeds on a straight unimpeded road.

1) sketch a
displacement/time graph of the events

2)
calculate the time and the distance transverse from the moment of the
original observation until the chase ends.

note: graph
paper is required for this solution.

Ans: 160 s
Ref FEB84

Ans: 5333.3
m

53. A cantilever beam is loaded as shown in the diagram below.
Neglecting the weight of the beam, sketch the shear force and
bending moment diagrams.

insert
diagram here

Ref MAR91

54. An axial thrust of 50 kN is carried by a plain collar type thrust
bearing, having inner and outer diameter of 250 mm, and 400 mm
respectively. Assuming that u
between the thrust surfaces is 0.02, and that the local wear rate of these
surfaces is proportional to the pressure and to the rubbing speed,
determine the power absorbed in friction at a speed of 120 rev/min.

Ans: 2.04
kW
Ref
Hannah p209

55. A bolt and nut falls into a deep tank and the sound of the
splash when it strikes the liquid is heard 2.2 seconds after. estimate the ullage of the tank if the velocity of sound is 335 m/s
at the ambient temperature of the air.

Ans: 22.324
m

56. A rectangular bar of uniform section 200 mm x 30 mm is used as a
structural member and is subjected to a tensile load of 500 kN at 5 mm to
one side of the 200 mm axis. Calculate:

1) the
maximum and minimum stress induced in the outer fibers
of the member

2) sketch
the stress distribution across the section

Ans:
95.8 MN/m2 (tensile)
208.3 MN/m2

Ans:
70.8 MN/m2
41.67 MN/m2

57. A simple pendulum consists of a spherical mass of 10 kg attached to
the end of a length of piano wires. The
upper end of the wire attached to a jewelled bearing arrangement on the
ceiling to reduce friction.

Disclaimer

Transport Canada has ask us to advise users of this webpage
to keep in mind that these questions are not the exact questions found in their
exams. Martin's Marine Engineering Page - www.dieselduck.net
is not affiliated with Transport Canada and these questions have been gathered
from various sources.